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Suppose a quantum version of gravity exists (which I don´t think). What will be the quantities in the uncertainty relation connected with this quantum gravity? Some time ago I sent a letter to Lee Smolin after which of course no answer came. But later I saw in an article that in his version (LQG) volume and area of space were the two quantities. Is this the case in all suggested types of quantized gravity?

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    $\begingroup$ "Suppose such a theory exists. What would it look like?" how could anyone know? $\endgroup$ – AccidentalFourierTransform Apr 2 '16 at 14:58
  • $\begingroup$ Be the first one to make a measurement that finds a quantization of spacetime and we will all be smarter... rest assured, if you do, Smolin will answer your mail. :-) $\endgroup$ – CuriousOne Apr 2 '16 at 15:01
  • $\begingroup$ @Curiousone Haha! :-) There still isn´t a quantum theory of gravity. And I think it´s not so that who does a measurement and finds a quantization of space-time (a measurement wich seems to me almost impossible) first is the smarter (and gets a lot of letters from Smolin, unless his theory wasn´t the right one). That doesn't rule out the possibility of fantasizing about the two quantities what the quantities are of the uncertainty relation of a specific theory. They´re not gonna be E and t and x and p, that´s for sure. These are the quantities for particles moving through space. $\endgroup$ – descheleschilder Apr 2 '16 at 20:21
  • $\begingroup$ No measurements, no physics... just phantasies. Mother nature is a woman, after all... if she doesn't want to be your girlfriend, then all you have are your dreams about her... $\endgroup$ – CuriousOne Apr 2 '16 at 21:16
  • $\begingroup$ But if she is my girlfriend, wich she is, I can fantasise about her and at the same time look what she is doing, touch her, smell her and listen to her. And maybe she doesn´t want to be your girlfriend if you measure her to deep. You must allow a good friend to have her secrets, and not want to know every little detail of her. Just having fantasies will suffice, wich will be in fact a good thing to maintain the relationship. Besides, how can you, in physics, make a measurement without having fantasised before what you are going to measure? Fantasy and measurement go hand in hand. $\endgroup$ – descheleschilder Apr 3 '16 at 15:22
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Models based on string theory have consistent quantization of gravity. Within these , there is theoretical work carried out for generalizing the uncertainty principle for quantum gravity.

One example :

GUP

It generalizes the usual space momentum uncertainty,(formula 15)

and another

GUP2

This one examines an uncertainty in space time, formula 2.2.

It is part of ongoing theoretical research.

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